Final answer:
The marginal cost (MC) is calculated by taking the derivative of the total cost function, which in this case is TC = 100 + 8Q + 0.01Q². The derivative of this function with respect to Q gives us the marginal cost function MC = 8 + 0.02Q.
Step-by-step explanation:
Marginal cost (MC) is the additional cost incurred by producing one more unit of output. It is calculated by taking the derivative of the total cost function with respect to quantity. In the given example, the total cost function is TC = 100 + 8Q + 0.01Q². To find the marginal cost, we need to take the derivative of this function with respect to Q.
To calculate the derivative, we use the power rule for differentiation. The derivative of 100 is 0, the derivative of 8Q is 8, and the derivative of 0.01Q² is 0.02Q. Therefore, the marginal cost function is MC = 8 + 0.02Q.
The marginal cost (MC) for firm A can be found by taking the derivative of the total cost (TC) function with respect to quantity (Q). The total cost function given is TC = 100 + 8Q + 0.01Q². By applying basic calculus rules, we find that the derivative of TC with respect to Q is MC = ∂8 + 0.02Q∂. Hence, the correct MC function for firm A is 8 + 0.02Q.